Who the hell doesn't have ID?
In the United States?
1) Elderly persons who no longer drive.
2) Urban residents who don't need a car to get where they're going.
3) University students who couldn't park on/near campus, even if they did have a car.
I actually fell into the third catagory for a midterm and a Presidential election, prior to getting my driver's license.
The second and third catagories are voting blocks that trend strongly Democratic and can be difficult to motivate to vote. Erecting roadblocks to that is a pretty naked voter-suppression tactic. It's even more exposed in states like Pennsylvania, where a driver's license is only a valid voter ID, if it was issued thirty days or more prior to the election, while a gun license is a valid voter ID from the moment it's issued. (Non-drivers trend Democratic, but non-driving gun-owners trend Republican.) It's more exposed still, when you note that there are larger vote fraud problems associated with absentee ballots, but none of the states instituting in-person voter ID requirements have implimented anything similar for absentee-voters, as absentee-voters tend to vote more reliably Republican than in-person voters. Then you get into the restrictions being placed on early voting in many of the same states as voter ID changes, and it just gets ludicrous.
Why the hell can someone vote without showing ID?
Because in the United States, voting is a privilege of citizenship, but holding a photo ID is not a responsibility of citizenship. The real question should be: Why should drivers, gun-carriers, and international travelers be a special class of citizen, while everyone else is reduced to a second-class status, who cannot vote?